Liquid dispenser systems, such as liquid soap and sanitizer dispensers, provide a user with a predetermined amount of liquid upon actuation of the dispenser. In addition, it is sometimes desirable to dispense the liquid in the form of foam by, for example, injecting air into the liquid to create a foamy mixture of liquid and air bubbles. Some liquids, such as, for example, alcohol-based liquids are difficult to foam and require enhanced mixing. Pumps for generating foam may form the foam by pumping a liquid and air mixture through a foam cartridge. Prior foam pumps and foam cartridges are disclosed in U.S. Published Patent Application No. 2014/0054323 filed on Mar. 9, 2013 and entitled Horizontal Pumps, Refill Units and Foam Dispensers with Integral Air Compressors, U.S. Pat. No. 8,955,718 filed on Mar. 18, 2013 and entitled Foam Pumps with Lost Motion and Adjustable Output Foam Pumps, U.S. Pat. No. 8,763,863 filed on Jul. 3, 2013 and entitled Bifurcated Foam Pump, Dispensers, and Refill Units, and U.S. Pat. No. 7,850,049 filed on Jan. 24, 2008 and entitled Foam Pump with Improved Piston Structure, all of which are incorporated herein by reference in their entirety.